Finite Group DatabasebetaFinite Group Databasebeta| order | 10836 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7×C9 · Schur multiplier (H2) = C1 |
| direct product | C7×Dic43⋊C9 |
| derived, Sylow | C43 ⋊ C4×C7×C9 |
| Hall | C7×C43⋊C9 ⋊ C4 |
| Hall | C7×Dic43 ⋊ C9 |
| Hall | C43⋊C9 ⋊ C4×C7 |
| Hall | C7×C43 ⋊ C4×C9 |
| Hall | Dic43 ⋊ C7×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C7 | D43⋊C3 |
| commutator, hypocenter | C43 | C4×C7×C9 |
| Frattini | C2×C3 | C7×D43⋊C3 |
| Fitting, socle, prime radical | C2×C3×C7×C43 | C2×C3 |
| cosocle | C2×C3×C43 | C2×C3×C7 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C2×C3×C7 | |
36 conjugacy classes of subgroups.
546 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10836, 8);